Related papers: Examples of Morphological Calculus
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
We say that there is a representation of the universal algebra B in the universal algebra A if the set of endomorphisms of the universal algebra A has the structure of universal algebra B. Therefore, the role of representation of the…
A construction of integration, function calculus, and exterior calculus is made, allowing for integration of unital magma valued functions against (compactified) unital magma valued measures over arbitrary topological spaces. The Riemann…
In this paper I consider the polymorpism of representations of universal algebra and tensor product of representations of universal algebra.
We give a general treatment of the master equation in homotopy algebras and describe the operads and formal differential geometric objects governing the corresponding algebraic structures. We show that the notion of Maurer-Cartan twisting…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
In this article we consider functions $f$ meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions. This condition simplifies and generalizes known conditions. We…
We reduce some key calculations of compositions of morphisms between Soergel bimodules ("Soergel calculus") to calculations in the nil Hecke ring ("Schubert calculus"). This formula has several applications in modular representation theory.
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
The formal group law of an elliptic curve has seen recent applications to computational algebraic geometry in the work of Couveignes to compute the order of an elliptic curve over finite fields of small characteristic. The purpose of this…
We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal problems on open subsets of Euclidean space in this setting we…
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…
We give a self-contained exposition of some mathematical aspects of the Mueller-Stokes formalism. In the first part we review some basic notions of linear algebra and establish a proper notation. In the second part we introduce the…
We develop geometry-of-numbers methods to count orbits in coregular vector spaces having bounded invariants over any global field. We apply these techniques to bound the average ranks and determine average Selmer group sizes of elliptic…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…